Solve x ^ 2 + 4x = (x ^ 2 + 4/2 * x) + 4/2 * x | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x^{2}+4x=(x^{2}+\frac{4}{2}x)+\frac{4}{2}x$$

Solve for x (complex solution)

$x\in \mathrm{C}$

Solution Steps

Divide $4$ by $2$ to get $2$.

$$x^{2}+4x=x^{2}+2x+\frac{4}{2}x$$

Divide $4$ by $2$ to get $2$.

$$x^{2}+4x=x^{2}+2x+2x$$

Combine $2x$ and $2x$ to get $4x$.

$$x^{2}+4x=x^{2}+4x$$

Subtract $x^{2}$ from both sides.

$$x^{2}+4x-x^{2}=4x$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$4x=4x$$

Subtract $4x$ from both sides.

$$4x-4x=0$$

Combine $4x$ and $-4x$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$

This is true for any $x$.

$$x\in \mathrm{C}$$

Solve for x

$x\in \mathrm{R}$

Solution Steps

Divide $4$ by $2$ to get $2$.

$$x^{2}+4x=x^{2}+2x+\frac{4}{2}x$$

Divide $4$ by $2$ to get $2$.

$$x^{2}+4x=x^{2}+2x+2x$$

Combine $2x$ and $2x$ to get $4x$.

$$x^{2}+4x=x^{2}+4x$$

Subtract $x^{2}$ from both sides.

$$x^{2}+4x-x^{2}=4x$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$4x=4x$$

Subtract $4x$ from both sides.

$$4x-4x=0$$

Combine $4x$ and $-4x$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$

This is true for any $x$.

$$x\in \mathrm{R}$$